The game runs near perfect, with no visible slowdown, even in Versus battles, but the game can't save. When I start a New Game it sais that a Save was created, but when I go to Versus Battle or Tournament Mode it sais that it can't load. Is there any solution to this problem. Oh and I think I have the NTSC version, but I am not sure.

Any time I go and create a new game, so I dont think that this will be the solution to the problem, but I'll try.
I just tried it. I went into the BIOS and deleted every file. When I went back to the game, I created a New Game and it still had problems loading from the memory card when I went to tournament mode(it probably tried to see if I had any characters unlocked).

I think you are not really undersanding what i said. game is saved on mecard1. It tries to load form gamecard2on tournament and it fail but thats not problem. If u want save just save it manually in options.